Question needed help with is 1.4-13. Please be detailed.

1.4-13. A manufacturing plant makes radios that each contain an integrated circuit (IC) supplied by three sources A, B, and C. The probability that the IC in a radio came from one of the sources is , the same for all sources. ICs ane known to be defective with probabilities 0.001, 0.003, and 0.002 for sources A, B, and C, respectively (a) What is the probability any given radio will contain a defective IC? (b) If a radio contains a defective IC, find the probability it came from source A. Repeat for sources B and C. 1.4-14. There are three special decks of cards. The first, deck Di, has all 52 cards of a regular deck. The second, D2, has only the 16 face cards of a regular deck (only 4 each of jacks, queens, kings, and aces). The third, D3, has only the 36 numbered cards of a regular deck (4 twos through 4 tens). A random experi- ment consists of first randomly choosing one of the three decks, then second, randomly choosing a card from the chosen deck. If P(D)-, P(D2)-and P(D) find the probabilities: (a) of drawing an ace, (b) of drawing a three, and (c) of drawing a red card. 1.5-1. Determine whether the three events A, B, and C of Example 1.4-1 are statis- tically independent. 1.5.2. List the various equations that four events Ai, A2, A3, and A4 must satisfy if they are to be statistically independent. 1.5-3. Given that two events A1 and A2 are statistically independent, show that (a) A is independent of A2 (b) Ai is independent of A2 (c) Ai is independent of A2 1.5-4. Show that there are 2N N-1 equations required in (1.5-6). (Hint: R that the binomial coefficient is the number of combinations of N things ta n at a time.) 15-5 In